Question: Luis works out for $\frac{3}{5}$ of an hour every day. To keep his exercise routines interesting, he includes different types of exercises, such as jumping jacks and squats, in each workout. If each type of exercise takes $\frac{3}{10}$ of an hour, how many different types of exercise can Luis do in each workout?
Solution: To find out how many types of exercise Luis could do in each workout, divide the total amount of exercise time ( $\frac{3}{5}$ of an hour) by the amount of time each exercise type takes ( $\frac{3}{10}$ of an hour). $ \dfrac{{\dfrac{3}{5} \text{ hour}}} {{\dfrac{3}{10} \text{ hour per exercise}}} = {\text{ number of exercises}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{3}{10} \text{ hour per exercise}}$ is ${\dfrac{10}{3} \text{ exercises per hour}}$ $ {\dfrac{3}{5}\text{ hour}} \times {\dfrac{10}{3} \text{ exercises per hour}} = {\text{ number of exercises}} $ $ \dfrac{{3} \cdot {10}} {{5} \cdot {3}} = {\text{ number of exercises}} $ Reduce terms with common factors by dividing the $3$ in the numerator and the $3$ in the denominator by $3$ $ \dfrac{{\cancel{3}^{1}} \cdot {10}} {{5} \cdot {\cancel{3}^{1}}} = {\text{ number of exercises}} $ Reduce terms with common factors by dividing the $10$ in the numerator and the $5$ in the denominator by $5$ $ \dfrac{{1} \cdot {\cancel{10}^{2}}} {{\cancel{5}^{1}} \cdot {1}} = {\text{ number of exercises}} $ Simplify: $ \dfrac{{1} \cdot {2}} {{1} \cdot {1}} = {2} $ Luis can do 2 different types of exercise per workout.